We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

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Interpretation Introduction Interpretation: How wander Waals equation simplifies to the ideal gas law under low pressure and high temperature should be explained. Concept introduction: By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law . According to ideal gas law, P V = n R T Where, P = pressure in atmospheres V= volumes in liters n = number of moles R =universal gas constant ( 0.08206 L ⋅ a t m / K ⋅ m o l ) T = temperature in kelvins Ideal gas law tends to hold best at low pressure and high temperature A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation. That is, [ P + a ( n V ) 2 ] ( V - n b ) = n R T ‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the individual gas a is a measure of intermolecular attraction b is a measure of size of the molecule Where, P = pressure in atmospheres V= volumes in liters n = number of moles R =universal gas constant ( 0 .08206L×atm/K×mol ) T = temperature in kelvins Explanation Explanation To explain: how wander Waals equation simplifies to the ideal gas law under low pressure and high temperature Van der Waals equation is [ P + a ( n V ) 2 ] ( V - n b ) = n R T By expanding the equation, [ P+ a n 2 V 2 ] × ( V - nb ) =n RT PV + a n 2 V V 2 -nbP - a n 3 b V 2 = nRT PV + an 2 V - nbP - a n 3 b V 2 = nRT At low pressure and high temperature molar volume of gas will be high

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Chemistry: An Atoms First Approach

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Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Chemistry: An Atoms First Approach

2nd Edition

Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Interpretation Introduction

Interpretation: How wander Waals equation simplifies to the ideal gas law under low pressure and high temperature should be explained.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L⋅atm/K⋅mol )

T = temperature in kelvins

Ideal gas law tends to hold best at low pressure and high temperature

A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation.

That is, [P+a(nV)2](V-nb) = nRT

‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the individual gas

a is a measure of intermolecular attraction
b is a measure of size of the molecule

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

Explanation of Solution

Explanation

To explain: how wander Waals equation simplifies to the ideal gas law under low pressure and high temperature

Van der Waals equation is

[P+a(nV)2](V-nb) = nRT

By expanding the equation,[P+ a n2V2] ×(V - nb) =n RTPV + a n2VV2-nbP - a n3bV2 = nRTPV + an2V- nbP - a n3bV2 = nRT

At low pressure and high temperature molar volume of gas will be high

We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

Chemistry: An Atoms First Approach

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Chemistry: An Atoms First Approach